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Description: Adjacency matrix of the Cayley graph of S 4, . generated by blue: (12) green: (13) red: (14) This is the corresponding graph, called the Nauru graph: . The red, green and blue squares form the permutation matrices, indexed 1, 5 and 21 in the following file.
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In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory.
PlantUML is an open-source tool allowing users to create diagrams from a plain text language. Besides various UML diagrams, PlantUML has support for various other software development related formats (such as Archimate, Block diagram, BPMN, C4, Computer network diagram, ERD, Gantt chart, Mind map, and WBD), as well as visualisation of JSON and YAML files.
The adjacency matrix of a complete bipartite graph K m,n has eigenvalues √ nm, − √ nm and 0; with multiplicity 1, 1 and n + m − 2 respectively. [12] The Laplacian matrix of a complete bipartite graph K m,n has eigenvalues n + m, n, m, and 0; with multiplicity 1, m − 1, n − 1 and 1 respectively. A complete bipartite graph K m,n has m ...
A sample DSM with 7 elements and 11 dependency marks. The design structure matrix (DSM; also referred to as dependency structure matrix, dependency structure method, dependency source matrix, problem solving matrix (PSM), incidence matrix, N 2 matrix, interaction matrix, dependency map or design precedence matrix) is a simple, compact and visual representation of a system or project in the ...
In algebraic graph theory, the adjacency algebra of a graph G is the algebra of polynomials in the adjacency matrix A(G) of the graph. It is an example of a matrix algebra and is the set of the linear combinations of powers of A. [1] Some other similar mathematical objects are also called "adjacency algebra".
An adjacency list representation for a graph associates each vertex in the graph with the collection of its neighbouring vertices or edges. There are many variations of this basic idea, differing in the details of how they implement the association between vertices and collections, in how they implement the collections, in whether they include both vertices and edges or only vertices as first ...